"publicity or press agent," 1945, also as a verb by that year, said to have been coined in show biz magazine "Variety" (but this is not the first attested use), supposedly from name of Gene Flack, a movie agent, but influenced by flak. There was a Gene Flack who was an advertising executive in the U.S. during the 1940s, but he seems to have sold principally biscuits, not movies.

flak

n.

1938, from German Flak, condensed from Fliegerabwehrkanone, literally "pilot warding-off cannon." Sense of "anti-aircraft fire" is 1940; metaphoric sense of "criticism" is c.1963 in American English.